Desdemona's father, Brabantio, is a rich and important Venetian politician. He likes Othello and invites him to visit his house a lot — but he never expected Othello "to steal" his daughter. Further, he never believed his little girl would marry Othello unless she was drugged or under some kind of spell.
Like many Shakespearean fathers (think Baptista Minola from The Taming of the Shrew or Portia's dad, who arranges his daughter's marriage from his grave in The Merchant of Venice), Brabantio tends to see his daughter as his property, which means that he sees marriage as a potential business transaction. Brabantio's irrational fears about his daughter's interracial marriage make him a central figure in the play's examination of race and sex, which you can read more about in our "Themes" section. Brabantio apparently dies of grief after his daughter runs off with Othello.